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Cambridge IGCSE Maths (0580) · Topic 4: Geometry · 4.5

Cambridge IGCSE Maths 0580 Symmetry Questions

Symmetry questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise symmetry →Symmetry notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Symmetry questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

For a regular hexagon, write down
(a) the number of lines of symmetry
(b) the order of rotational symmetry.

Show the worked answer
  1. A regular polygon with \(n\) sides has \(n\) lines of symmetry and rotational symmetry of order \(n\).

Answer: (a) \(6\) (b) \(6\)

Question 2 Core non-calculator · easy

A rhombus has no right angles. Write down
(a) its number of lines of symmetry
(b) its order of rotational symmetry.

Show the worked answer
  1. (a) Its two diagonals are lines of symmetry. (The lines through the midpoints of opposite sides are not.)
  2. (b) It looks the same after a half turn and a full turn.

Answer: (a) \(2\) (b) \(2\)

Question 3 Core non-calculator · easy

A parallelogram has no right angles and its sides are not all equal. Write down
(a) its number of lines of symmetry
(b) its order of rotational symmetry.

Show the worked answer
  1. (a) No fold maps it onto itself.
  2. (b) A half turn about its centre maps it onto itself.

Answer: (a) \(0\) (b) \(2\)

Question 4 Core non-calculator · easy · 2 marks

A road sign is a regular octagon. How many lines of symmetry does the sign have, and what is its order of rotational symmetry?

Show the answer and mark scheme
  • B1 8 lines
  • B1 order 8

Answer: 8 lines, order 8

Question 5 Core non-calculator · medium

An isosceles trapezium is drawn. Write down
(a) its number of lines of symmetry
(b) its order of rotational symmetry.

Show the worked answer
  1. (a) One line, through the midpoints of the two parallel sides.
  2. (b) It only fits onto itself after a full turn: order \(1\).

Answer: (a) \(1\) (b) \(1\)

Question 6 Core non-calculator · medium · 2 marks

Write down the name of a quadrilateral that has

(a) 4 lines of symmetry and rotational symmetry of order 4

(b) exactly 1 line of symmetry and rotational symmetry of order 1.

Show the answer and mark scheme
  • B1 (a) square
  • B1 (b) kite (or isosceles trapezium)

Answer: (a) square (b) kite (or isosceles trapezium)

Symmetry questions: Extended

Extended content, for Papers 2 and 4. Core students can skip these.

Question 7 Extended non-calculator · medium

How many planes of symmetry does
(a) a cuboid with three different edge lengths have
(b) a cube have?

Show the worked answer
  1. (a) One plane through the middle parallel to each pair of faces: \(3\).
  2. (b) Those \(3\), plus \(6\) diagonal planes through opposite edges: \(9\).

Answer: (a) \(3\) (b) \(9\)

Question 8 Extended non-calculator · medium

A prism has an equilateral triangle as its cross-section.
How many planes of symmetry does it have?

Show the worked answer
  1. \(3\) planes along the length, one through each line of symmetry of the triangle.
  2. \(1\) plane across the middle, parallel to the triangular ends.

Answer: \(4\)

Question 9 Extended non-calculator · hard

A pyramid has a square base and its apex is directly above the centre of the base.
(a) How many planes of symmetry does it have?
(b) What is the order of rotational symmetry about its vertical axis?

Show the worked answer
  1. (a) Two planes through the apex and the midpoints of opposite base edges, and two through the apex and opposite corners: \(4\).
  2. (b) A quarter turn about the vertical axis maps it onto itself: order \(4\).

Answer: (a) \(4\) (b) \(4\)

Question 10 Extended non-calculator · hard · 2 marks

A right pyramid has a base that is a regular hexagon.

(a) How many planes of symmetry does it have?

(b) What is the order of rotational symmetry about its vertical axis?

Show the answer and mark scheme
  • B1 (a) 6
  • B1 (b) 6

Answer: (a) 6 (b) 6

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test symmetry?

Symmetry is on both tiers (syllabus 4.5), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more symmetry questions?

In the 0580 practice for topic 4 (Geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More geometry questions